CLS-28

Reduced mass

Two-body reduction.

Reading speed

GoverningReduced mass

Governing equation

\mu=m_1 m_2/(m_1+m_2)

$m2 \in \left[0.1, 40\right]$

where

m1: m1 (kg)
m2: m2 (kg)
mu: Reduced mass (kg)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mu=m_1 m_2/(m_1+m_2)

$m2 \in \left[0.1, 40\right]$

$m2 = 0.1$ $mu = 0.098$

Along the curve

②

Domain of the variable — blue

m2_{\min} = 0.1,\quad m2_{\max} = 40

$m2 \in \left[0.1, 40\right]$

$m2 = 0.1$ $m2 = 0.1$

Along the curve

③

Response curve — green

\mu=m_1 m_2/(m_1+m_2)

$m2 \in \left[0.1, 40\right]$

$m2 = 0.1$ $mu = 0.098$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}mu}{\mathrm{d}m2}

$m2 \in \left[0.1, 40\right]$

$m2 = 0.351$ $mu^{\prime} = 0.848$

Along the curve

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-28 — Reduced mass) is the form associated with Reduced mass. Working symbols: $m1$ , $m2$ $\rightarrow$ $mu$ . Two-body reduction. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

mu

from

m1

m2

in Classical mechanics via

\mu=m_1 m_2/(m_1+m_2)

Two-body reduction. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

m1 = 4.000\,\mathrm{kg}

m2 = 6.000\,\mathrm{kg}

, the governing relation

\mu=m_1 m_2/(m_1+m_2)

yields

mu = 2.400\,\mathrm{kg}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

m1 m14 kgm2 m26 kg

Outputs

Reduced mass mu2.400 kg

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Two-body reduction. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube